Petrol bombs were thrown at the entrance to the City Cemetery.
Both nationalist and unionist politicians condemned the violence.
The PSNI said it had made arrests after a notified parade in the city earlier today.
“Five men, aged, 29, 38, 40, 50 and 54 years old, were arrested under the Terrorism Act,” a police statement said.
“A sixth man, aged 40 years old, was arrested on suspicion of disorderly behaviour. All six men remain in custody this evening. Police seized a number of vehicles, suspected terrorist uniforms and petrol bombs.”
The commander for Derry and Strabane District, Chief Superintendent Ryan Henderson said: “Earlier today, police were in attendance at a notified parade in the city. On the basis of initial observations, participants in the parade were assessed as having potentially committed criminal offences. Police monitored the event closely and, at what was considered to be an appropriate point, took action to secure evidence and make arrests.
“Whilst doing so, police officers came under attack from petrol bombs and masonry.
“Our officers showed tremendous courage and professionalism in what was still clearly a dangerous situation.”
Earlier, the family of the murdered journalist Lyra McKee voiced disgust that a republican Easter parade linked with dissidents went ahead on the anniversary of her murder.
Ms McKee, a journalist, died after being struck by a bullet during rioting in the Creggan area of Derry on April 18, 2019.
SDLP leader and Foyle MP Colum Eastwood said: “Today is the third anniversary of the murder of Lyra McKee on the streets of our city. A young journalist who was trying to make a life for herself in Derry and who had so much to give to our community.
“Lyra’s memory continues to galvanise our resolve against the men of violence who prey on bigotry and hate. Derry stands with Lyra’s family, with Sara and with everyone who knew her today.
“The scenes from the city cemetery this afternoon are absolutely and totally wrong. Young people in our city are being manipulated into carrying out violent attacks against police officers by people who are intent on dragging this city and its people backwards. We wont let them win.”
Superintendent Henderson said: “Fortunately, none of our officers, or members of the public were injured as a result of this reckless and criminal behaviour. Our enquiries will continue over the coming days and weeks to bring offenders to justice.”
Mr Eastwood said: “Those responsible for orchestrating a very clearly pre-arranged attack on police wanted to create a violent standoff this afternoon. They want to whip up division, fear and resentment because it’s the only way they can gain a foothold in our community. They need to understand that those days are long gone and they aren’t coming back. The people of Derry want to live in peace with their neighbours. We wont have that peace threatened by anyone, let alone cowards that send kids out to throw petrol bombs.”
Vigils took place in Lyra McKee’s memory in Belfast and Derry yesterday.
AnThe New IRA has previously claimed it was responsible for killing the journalist and author.
The republican parade to commemorate the 1916 Easter Rising that took place in Derry today was connected to the group Saoradh.
The Parades Commission had ruled that no paramilitary style clothing be worn in the procession.
Ms McKee’s sister Nichola Corner questioned why the event could not have been held on a different day, pointing out the date of Easter changes every year.
“When we objected to this parade taking place, it was on the grounds of the date alone, not on the grounds of marching,” she told the PA news agency.
“Had they marched on Saturday, Sunday, Tuesday, we wouldn’t have cared. It is insulting to go forth on Lyra’s anniversary, to do a parade of this nature honouring other dead. It’s in really bad taste.”